Method for determining the efficiency of nucleic acid amplifications

ABSTRACT

The present invention concerns a method for determining the efficiency of the amplification of a target nucleic acid comprising the following steps: (i) preparation of a dilution series of the target nucleic acid, (ii) amplifying the target nucleic acid under defined reaction conditions, the amplification being measured in real-time (iii) setting a defined signal threshold value, (iv) determining the cycle number at which the signal threshold value is exceeded for various dilutions, (v) determining the amplification efficiency as a function of the amount of original target nucleic acid. The present invention also concerns a method for the quantification of a target nucleic acid in a sample in which the efficiency of the amplification reaction is determined in this manner and is taken into account in the quantification.

The present application claims priority to co-pending European PatentApplication No. 00107036.6, filed Mar. 31, 2000, co-pending GermanPatent Application No. 10034209.4, filed Jul. 13, 2000, and co-pendingGerman Patent Application No. 10045521.2, filed Sep. 13, 2000, each ofwhich is incorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present invention relates to the field of nucleic acidquantification with the aid of quantitative real-time PCR.

BACKGROUND OF THE INVENTION

Methods for the quantification of nucleic acids are important in manyareas of molecular biology and in particular for molecular diagnostics.At the DNA level such methods are used for example to determine the copynumbers of gene sequences amplified in the genome. However, methods forthe quantification of nucleic acids are used especially in connectionwith the determination of mRNA quantities since this is usually ameasure for the expression of the respective coding gene.

If a sufficient amount of sample material is available, special mRNAscan be quantified by conventional methods such as Northern Blot analysisor RNAse protection assay methods. However, these methods are notsensitive enough for sample material that is only available in smallamounts or for genes that express very weakly.

The so-called RT-PCR is a much more sensitive method. In this method asingle-stranded cDNA is firstly produced from the mRNA to be analysedusing a reverse transcriptase. Subsequently a double-stranded DNAamplification product is generated with the aid of PCR.

A distinction is made between two different variants of this method:

-   -   In the so-called relative quantification the ratio of the        expression of a certain target RNA is determined relative to the        amount of RNA of a so-called housekeeping gene which is assumed        to be constitutively expressed in all cells independent of the        respective physiological status. Hence the mRNA is present in        approximately the same amount in all cells. The advantage of        this is that different initial qualities of the various sample        materials and the process of RNA preparation has no influence on        the particular result. However, an absolute quantification is        not possible with this method.    -   Alternatively the absolute amount of RNA used can be determined        with the aid of standard nucleic acids of a known copy number        and amplification of a corresponding dilution series of this        standard nucleic acid. There are two alternatives:

When using external standards the standard and target nucleic acid areamplified in separate reaction vessels. In this case a standard can beused with an identical sequence to the target nucleic acid. However,systematic errors can occur in this type of quantification if the RNApreparation to be analysed contains inhibitory components which impairthe efficiency of the subsequent PCR reaction. Such errors can beexcluded by using internal standards i.e. by amplifying the standard andtarget nucleic acid in one reaction vessel. However, a disadvantage ofthis method is that standards have to be used that have differentsequences compared to the target nucleic acid to be analysed in order tobe able to distinguish between the amplification of the standard andtarget nucleic acid. This can in turn lead to a systematic error in thequantification since different efficiencies of the PCR amplificationcannot be excluded when the sequences are different.

PCR products can be quantified in two fundamentally different ways:

a) End point determination of the amount of PCR product formed in theplateau phase of the amplification reaction

In this case the amount of PCR product formed does not correlate withthe amount of the initial copy number since the amplification of nucleicacids at the end of the reaction is no longer exponential and instead asaturation is reached. Consequently different initial copy numbersexhibit identical amounts of PCR product formed. Therefore thecompetitive PCR or competitive RT-PCR method is usually used in thisprocedure. In these methods the specific target sequence is coamplifiedtogether with a dilution series of an internal standard of a known copynumber. The initial copy number of the target sequence is extrapolatedfrom the mixture containing an identical PCR product quantity ofstandard and target sequence (Zimmermann and Mannhalter, Bio-Techniques21:280-279, 1996). A disadvantage of this method is also thatmeasurement occurs in the saturation region of the amplificationreaction.

b) Kinetic real-time quantification in the exponential phase of PCR.

In this case the formation of PCR products is monitored in each cycle ofthe PCR. The amplification is usually measured in thermocyclers whichhave additional devices for measuring fluorescence signals during theamplification reaction. A typical example of this is the RocheDiagnostics LightCycler (Cat. No. 20110468). The amplification productsare for example detected by means of fluorescent labelled hybridizationprobes which only emit fluorescence signals when they are bound to thetarget nucleic acid or in certain cases also by means of fluorescentdyes that bind to double-stranded DNA. A defined signal threshold isdetermined for all reactions to be analysed and the number of cycles Cprequired to reach this threshold value is determined for the targetnucleic acid as well as for the reference nucleic acids such as thestandard or housekeeping gene. The absolute or relative copy numbers ofthe target molecule can be determined on the basis of the Cp valuesobtained for the target nucleic acid and the reference nucleic acid(Gibson et al., Genome Research 6:995-1001; Bieche et al., CancerResearch 59:2759-2765, 1999; WO 97/46707; WO 97/46712; WO 97/46714).Such methods are also referred to as a real-time PCR.

In summary in all the described methods for the quantification of anucleic acid by PCR the copy number formed during the amplificationreaction is always related to the copy number formed of a referencenucleic acid which is either a standard or an RNA of a housekeepinggene. In this connection it is assumed that the PCR efficiency of thetarget and reference nucleic acid are not different.

Usually a PCR efficiency of 2.00 is assumed which corresponds to adoubling of the copy number per PCR cycle (User Bulletin No. 2 ABI Prism7700, PE Applied Biosystems, 1997).

However, it has turned out that the real PCR efficiency can be differentfrom 2.00 since it is influenced by various factors such as the bindingof primers, length of the PCR product, G/C content and secondarystructures of the nucleic acid to be amplified and inhibitors that maybe present in the reaction mixture as a result of the samplepreparation. This is particularly relevant when using heterologousreference nucleic acids e.g. in the relative quantification compared tothe expression of housekeeping genes. Moreover it is also not knownwhether or to what extent the initial concentration of the targetnucleic acid to be detected significantly influences the efficiency ofan amplification reaction.

SUMMARY OF THE INVENTION

The object of the present invention was therefore to provide a method todetermine the efficiency of nucleic acid amplifications as exactly aspossible and its use in methods for the exactest possible quantificationof nucleic acids.

This object is achieved according to the invention by a method fordetermining the efficiency of the amplification of a target nucleic acidwherein

a) a dilution series of the target nucleic acid is prepared

b) the target nucleic acid is amplified under defined reactionconditions and the amplification is measured in real-time

c) a defined signal threshold value is set

d) for each dilution the cycle number is determined at which the signalthreshold value is exceeded,

e) the amplification efficiency is determined as a function of theoriginal amount of target nucleic acid.

Thus the amplification efficiency can be determined by generating anon-linear continuously differentiable function of a logarithm of thecopy number of target nucleic acid used for the amplification as afunction of the cycle number at which the signal threshold value isexceeded and from this function the amplification efficiency E iscalculated as a function of the amount of target nucleic acid. In thisembodiment the amplification efficiency E of a certain amount of targetnucleic acid is preferably determined as the negative local firstderivative of the continuously-differentiable function from step e).

Alternatively the amplification efficiency can also be determined bydetermining a non-linear continuously differentiable function of thedetermined cycle numbers as a function of the logarithm of the copynumbers of target nucleic acid used for the amplification andcalculating the amplification efficiency E from the determined function.In this case the amplification efficiency E of a certain amount oftarget nucleic acid is preferably determined as the reciprocal negativelocal first derivative of the continuously differentiable function fromstep e).

Methods have proven to be particularly advantageous in which theamplification efficiency is determined as a function of the logarithm ofthe concentration of the target nucleic acid or vice versa with the aidof a polynomial fit to determine the non-linear continuouslydifferentiable function. This can be a polynomial fit of the 3^(rd),4^(th), 5^(th), 6^(th), or 7^(th) degree or preferably a fit of the4^(th) degree.

Hence methods according to the invention for the quantification of atarget nucleic acid in a sample comprise the following steps:

a) Determination according to the invention of the amplificationefficiency of the target nucleic acid under defined conditions.

b) Amplification of the target nucleic acid contained in the sampleunder the same reaction conditions.

c) Measurement of the amplification in real-time.

d) Quantification of the original amount of target nucleic acid in thesample by correction of the original amount derived from step c) withthe aid of the determined amplification efficiency.

These methods can be used for relative quantification in comparison tothe expression of housekeeping genes as well as for absolutequantification.

According to the invention methods for the absolute quantification ofthe target nucleic acid in a sample comprise the following steps:

a) Determination according to the invention of the amplificationefficiencies of the target nucleic acid and of an internal or externalstandard under defined amplification conditions.

b) Amplification of the target nucleic acid contained in the sample andof the internal or external standard under the same defined reactionconditions.

c) Measurement of the amplification of the target nucleic acid andstandard in real-time.

d) Calculation of the original copy number in the sample by correctionof the copy number derived in step c) with the aid of the amplificationefficiencies determined in step a).

In contrast methods for the quantification of a target nucleic acid in asample relative to a reference nucleic acid comprise the followingsteps.

a) Determination according to the invention of the amplificationefficiencies of the target nucleic acid and of the reference nucleicacid under defined amplification conditions.

b) Amplification of the target nucleic acid contained in the sample aswell as of the reference nucleic acid contained in the sample under thesame defined amplification conditions.

c) Measurement of the amplification of the target nucleic acid and ofthe reference nucleic acid in real-time.

d) Calculation of the original ratio of target nucleic acid andreference nucleic acid in the sample by correction of the ratio derivedfrom step c) with the aid of the amplification efficiencies determinedin step a).

The invention additionally concerns all methods in which thedetermination of the amplification efficiencies is only indirectly usedfor the quantification result and in particular one which is dependenton the initial concentration. In this sense the invention concerns inparticular a method for the relative quantification of a target nucleicacid relative to a reference nucleic acid and standardized withreference to a calibrator sample comprising the following steps:

a) Preparation of one common or two separate dilution series of targetnucleic acid and reference nucleic acid.

b) Amplification of the various dilutions of target nucleic acid andreference nucleic acid under defined reaction conditions, theamplification of the nucleic acid being measured in real-time.

c) Setting defined signal threshold values for the target nucleic acidand reference nucleic acid.

d) Determining the cycle numbers Cp at which the defined signalthreshold values for the target nucleic acid and reference nucleic acidare exceeded in each dilution.

e) Determination of a continuously differentiable function of thelogarithm of the amount of target nucleic acid used as a function of theCp values determined in d) and determination of a continuouslydifferentiable function of the logarithm of the amounts of referencenucleic acid used as a function of the determined Cp values.

f) Determination of the Cp values of the target nucleic acid andreference nucleic acid in the sample to be analysed as well as in acalibrator sample.

g) Assignment of the Cp values measured in step f) to particularfunction values of the functions determined in step e).

h) Determining the quotients of the function values from g) of thetarget nucleic acid and reference nucleic acid for the sample to beanalysed as well as for the calibrator sample.

i) Determination of the ratio of the quotients from h) as a measure forthe original amount of target DNA contained in the sample.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1:

Schematic representation of a function for determining the logarithm ofa relative concentration versus the determined cycle number.

FIG. 2 a:

Determination of the amplification efficiency of CycA by determining aregression line.

FIG. 2 b:

Determination of the amplification efficiency of PBGD by determining aregression line.

FIG. 3 a:

Efficiency correction for the amplification of CycA with the aid of apolynomial fit of the 4^(th) degree.

FIG. 3 b:

Efficiency correction for the amplification of PBGD with the aid of apolynomial fit of the 4^(th) degree.

DETAILED DESCRIPTION OF THE INVENTION

A) Requirement for a Target-dependent Efficiency Correction

The importance of an efficiency correction for quantitative nucleic acidamplification methods will be illustrated by an error calculation. Table1 shows a theoretical calculation of the average percentage error of thedetermined copy number in the case of amplification efficiencies thatare different from 2.00 in relation to the respective cycle number. Theerror is calculated according to the formulapercentage error=(2^(n) /E ^(n)−1)×100

in which E is the efficiency of the amplification and n is therespective cycle number at which the percentage error is determined.TABLE 1 PCR efficiency Detection Cycle (n) (E) 10 15 20 25 30 35 2.00 —— — — — — 1.97 16% 25% 35%    46%    57%    70% 1.95 29% 46% 66%    88%  113%    142% 1.90 67% 116% 179%   260%   365%    500% 1.80 187% 385%722%   1290%   2260%   3900% 1.70 408% 1045% 2480%   5710% 13.000% 29.500% 1.60 920% 2740% 8570% 26.400% 80.700% 246.400%

The amplification efficiency of a PCR reaction can be determined byvarious methods.

For example in the case of a real-time monitoring of PCR reactions thiscan be achieved by determining the amount of amplified target nucleicacid in each amplification cycle and determining the efficiency of theamplification reaction from the resulting values.

Alternatively the efficiency of the amplification reaction of aparticular target can be determined in a real-time PCR mode underdefined conditions by firstly amplifying various dilutions of the targetnucleic acid and determining the cycle number for each dilution at whicha previously defined signal threshold value is exceeded.

The efficiency is then determined from the slope of the function of thelogarithm of the copy number used versus the cycle number determined forthe respective copy number. An advantage of this method is that asystematic error cannot occur that results from determining theamplification efficiency in a phase of the PCR reaction in which thereis no longer an exponential amplification of the target nucleic acid(plateau phase).

However, it unexpectedly turned out that under certain circumstances theamplification efficiency can also be dependent on the original amount oftarget nucleic acid. An obvious change in the amplification efficiencyis found especially at low concentrations in the correspondingexperimental preparations. Consequently the methods described above fordetermining the efficiency do not result in linear functions so that inthese cases the described determination of the slope of the regressionline would for example result in values for the determined amplificationefficiencies that are too low especially at low concentrations of targetnucleic acid.

Due to the dependence of the amplification efficiency on theconcentration of the target nucleic acid, it is not possible to rule outa change in the amplification efficiency even already during the firstcycles of an amplification reaction although it is still in anexponential phase. Since, however, this phenomenon cannot be directlyexperimentally analysed due to a lack of detection sensitivity, aconcentration-dependent amplification efficiency is understood in thefollowing as the amplification efficiency determined by means of theelapsed cycles at the respective detection time point.

B) Absolute and Relative Quantification

The present invention therefore concerns methods for theefficiency-corrected quantification of nucleic acids in which theefficiency of the amplification is determined by

a) preparing a dilution series of the target nucleic acid

b) amplifying the target nucleic acid under defined reaction conditionsas claimed in claim 1 and measuring the amplification of the nucleicacid in real-time

c) setting a defined signal threshold value

d) for each dilution determining the cycle number Cp at which the signalthreshold value is exceeded and

e) determining the amplification efficiency as a function of the amountof target nucleic acid.

In particular the amplification efficiency can be determined as afunction of the original amount of target nucleic acid by

-   -   a non-linear continuously differentiable function of a logarithm        of the copy number of target nucleic acid used for the        amplification as a function of the copy number at which the        signal threshold value is exceeded or alternatively a non-linear        continuously differentiable function of the determined cycle        number as a function of the logarithm of the copy number of        target nucleic acid used in each case and    -   calculating the amplification efficiency E from the determined        function. The respective amplification efficiency is determined        according to the invention as a function of the amount of target        nucleic acid that is used in each case.

The continuous function is determined by suitable mathematical methodsand algorithms. For example the function can be described by apolynomial fit of higher degree. A polynomial fit of the 3^(rd), 4^(th),5^(th), 6^(th) or 7^(th) degree has proven to be suitable forcalculating a function, a polynomial fit of the 4^(th) order beingpreferred.

The efficiency which depends on the target amounts can be determined byderivation of a continuously differentiable function F(Cp) of the Cpvalues as a function of a logarithm of the original copy number or viceversa.

The amplification efficiency can then be determined according to theequationE=G^(−f(Cp))in which f(Cp) is the derivative of the continuous function and G is thebase number of the logarithm. Hence in this embodiment the amplificationefficiency E of a certain original amount of target nucleic acid isdetermined as the negative local first derivative of the previouslydetermined continuously differentiable function.

Alternatively the amplification efficiency E can be determined accordingto the equation$E = {G^{-}\frac{1}{f^{\prime}( {\log({conc})} )}}$in which conc is the original amount of the nucleic acid, f(log(conc))is the derivative of the continuous function and G is the base number ofthe logarithm. Hence in this embodiment the amplification efficiency Eof a certain original amount of target nucleic acid is determined as thereciprocal negative local first derivative of the previously determinedcontinuously differentiable function.

The efficiency-corrected quantification of nucleic acids as a functionof the amount of target nucleic acid can in principle be used formethods for absolute quantification as well as for methods for relativequantification. Moreover such an efficiency correction is alsoparticularly advantageous in methods in which a relative quantificationis standardized on the basis of a so-called calibrator sample (ABI Prism7700 Application Manual, Perkin Elmer) in order to eliminate theinfluence of different detection sensitivities for the target andreference nucleic acid.

If it is intended to determine the absolute amount of target nucleicacid to be detected in the sample, the method for quantifying a targetnucleic acid in a sample according to the invention comprises thefollowing steps:

a) Determination of the amplification efficiencies of the target nucleicacid and of an internal or external standard as a function of theirrespective initial concentrations under defined amplificationconditions.

b) Amplification of the target nucleic acid contained in the sample andof the internal or external standard under the same defined reactionconditions.

c) Measurement of the amplification of the target nucleic acid andstandard in real-time.

d) Calculation of the original copy number in the sample by correctionof the copy number derived in step c) with the aid of the amplificationefficiencies determined in step a).

The sequences of the target nucleic acid and standard nucleic acid areadvantageously substantially identical. However, when selecting thesequence for an internal standard it must be taken into account that theavailable detection system is able to distinguish between the standardand target nucleic acid. This can for example be achieved by usinghybridization probes with different labels for the detection of thetarget nucleic acid and internal standard. Ideally oligonucleotides areused for this as detection probes which can be used to distinguishbetween minimal sequence differences such as point mutations.

An advantage of using an internal standard is that the inhibitorspresent in the sample also influence the amplification of the standard.Hence differences in the amplification efficiencies can be minimized.

In contrast the use of an external standard has the advantage that theamplification reactions of the target nucleic acid and standard cannotcompetitively interfere with one another with regard to theirefficiency. Moreover the amplification products of the standard andtarget nucleic acid can be detected in parallel reaction mixes with theaid of the same detection system for example with the same hybridizationprobe. A disadvantage is possible differences in the PCR efficienciesdue to inhibitors in the sample. However, errors in the quantificationcaused by this can be eliminated by an efficiency correction accordingto the invention.

A subject matter of the present invention in relation to relativequantification is also a method for the quantification of a targetnucleic acid in a sample relative to a reference nucleic acid comprisingthe following steps:

a) Determination of the amplification efficiencies of the target nucleicacid and of the reference nucleic acid as a function of their respectiveinitial concentrations under defined amplification conditions.

b) Amplification of the target nucleic acid contained in the sample aswell as of the reference nucleic acid contained in the sample under thesame defined amplification conditions.

c) Measurement of the amplification of the target nucleic acid and ofthe reference nucleic acid in real-time.

d) Calculation of the original ratio of target nucleic acid andreference nucleic acid in the sample by correction of the ratio derivedfrom step c) with the aid of the amplification efficiencies determinedin step a).

Such a method according to the invention eliminates on the one hand theinfluence of inhibitors that may be present in the examined sample and,on the other hand, corrects errors which may occur as a result ofdifferent amplification efficiencies of the target nucleic acid andreference nucleic acid.

An essential requirement for this method according to the invention forrelative quantification is that the amplification efficiency of thetarget nucleic acid as well as the amplification efficiency of thereference nucleic acid is determined as a function of the amount oftarget and reference nucleic acid that was originally present. Both ofthese determinations are preferably carried out by the method describedabove by determining the cycle number at which a certain signalthreshold value is exceeded.

In a preferred embodiment of relative quantification the sample isdivided into two aliquots and the real-time measurement of theamplification of the target nucleic acid and reference nucleic acid iscarried out in separate reaction vessels. This prevents interferencebetween the amplification reactions of the target nucleic acid and thereference nucleic acid with regard to their efficiency for example bycompetition for deoxynucleotides or Taq polymerase. Furthermore thetarget nucleic acid and reference nucleic acid can be detected with thesame detection systems for example with the same DNA binding dye.

Alternatively the real-time measurement of the amplification of targetnucleic acid and reference nucleic acid can be carried out from onesample in the same reaction vessel using differently labelledhybridization probes. This is particularly advantageous when only smallamounts of sample material are available because the number of PCRreactions required is halved in this manner.

Steps b) to d) are advantageously carried out in a parallel mixturecontaining a so-called calibrator sample. The calibrator sample is asample which contains the target nucleic acid and reference nucleic acidin a defined ratio that is constant for each measurement. Subsequentlythe ratio of the quotients determined for the sample and for thecalibrator sample is determined as a measure for the original amount oftarget nucleic acid in the sample. This has the advantage that inaddition other systematic errors are eliminated that are due todifferences in the detection sensitivity of the target nucleic acid andreference nucleic acid. Such systematic errors can for example occur asa result of different hybridization properties of the hybridizationprobes or , in the case of fluorescent-labelled probes, differentexcitation efficiencies, quantum yields or coupling efficiencies of thedye to the probe. Therefore the sample to be tested and the calibratorsample must be analysed in each experiment with the same detectionagents i.e. with the same batch of fluorescent-labelled hybridizationprobes.

The invention in particular also concerns those embodiments of thedescribed methods for the efficiency-corrected quantification of nucleicacids in which the amplification products are detected by hybridizationprobes which can be labelled with a detectable component in manydifferent ways.

A prerequisite for the efficiency-corrected determination of theoriginal amount of a target nucleic acid and for the determination ofthe amplification efficiencies per se is to set signal threshold valuesand subsequently determine the cycle number for the respectiveamplification reaction at which a certain signal threshold value isreached. The signal threshold value can be determined according to theprior art in various ways:

According to the prior art the signal threshold value can for example bea signal which corresponds to a certain multiple of the statisticalvariance of the background signal (ABI Prism 7700 Application Manual,Perkin Elmer).

Alternatively the cycle number at which the signal threshold value isexceeded can be determined according to the so-called “fit point abovethreshold” method (LightCycler Operator's Manual, B59-B68, RocheMolecular Biochemicals, 1999).

In a further embodiment the threshold value can be determined as arelative value instead of an absolute value when, independently of theabsolute value of the signal, the course of the amplification reactionis determined as a function of the cycle number and subsequently then^(th) derivative is calculated. In this case exceeding certain extremescan be defined as exceeding a certain signal threshold value (EPApplication No. 00106523.4). Hence this method of determining thethreshold value is independent of the absolute signal strength of forexample a fluorescence signal. Thus it is particularly suitable forthose embodiments in which the target nucleic acid and reference nucleicacid are amplified in the same reaction vessel and are detected with theaid of different fluorescent labels. Methods have proven to beparticularly suitable for the efficiency-corrected quantification of PCRproducts in which the maximum of the second derivative is determined asa measure for the signal threshold value.

The hybridization probes used for the method according to the inventionare usually single-stranded nucleic acids such as single-stranded DNA orRNA or derivatives thereof or alternatively PNAs which hybridize at theannealing temperature of the amplification reaction to the targetnucleic acid. These oligonucleotides usually have a length of 20 to 100nucleotides.

The labelling can be introduced on any ribose or phosphate group of theoligonucleotide depending on the particular detection format. Labels atthe 5′ and 3′ end of the nucleic acid molecule are preferred.

The type of label must be detected in the real-time mode of theamplification reaction. This is for example in principle also (but notonly) possible with the aid of labels that can be detected by NMR.

Methods are particularly preferred in which the amplified nucleic acidsare detected with the aid of at least one fluoresent-labelledhybridization probe.

Many test procedures are possible. The following three detection formatshave proven to be particularly suitable in connection with the presentinvention:

(i) FRET Hybridization Probes

For this test format 2 single-stranded hybridization probes are usedsimultaneously which are complementary to adjacent sites of the samestrand of the amplified target nucleic acid. Both probes are labelledwith different fluorescent components. When excited with light of asuitable wavelength, a first component transfers the absorbed energy tothe second component according to the principle of fluorescenceresonance energy transfer such that a fluorescence emission of thesecond component can be measured when both hybridization probes bind toadjacent positions of the target molecule to be detected.

Alternatively it is possible to use a fluorescent-labelled primer andonly one labelled oligonucleotide probe (Bernard et al., AnalyticalBiochemistry 235, p. 1001-107 (1998)).

(ii) TaqMan Hybridization Probes

A single-stranded hybridization probe is labelled with two components.When the first component is excited with light of a suitable wavelength,the absorbed energy is transferred to the second component, theso-called quencher, according to the principle of fluorescence resonanceenergy transfer. During the annealing step of the PCR reaction, thehybridization probe binds to the target DNA and is degraded by the 5′-3′exonuclease activity of the Taq polymerase during the subsequentelongation phase. As a result the excited fluorescent component and thequencher are spatially separated from one another and thus afluorescence emission of the first component can be measured.

(iii) Molecular Beacons

These hybridization probes are also labelled with a first component andwith a quencher, the labels preferably being located at both ends of theprobe. As a result of the secondary structure of the probe, bothcomponents are in spatial vicinity in solution. After hybridization tothe target nucleic acids both components are separated from one anothersuch that after excitation with light of a suitable wavelength thefluorescence emission of the first component can be measured (Lizardi etal., U.S. Pat. No. 5,118,801).

In the described embodiments in which only the target nucleic acid oronly the reference nucleic acid or an external standard is amplified inone reaction vessel in each case, the respective amplification productcan also be detected according to the invention by a DNA binding dyewhich emits a corresponding fluorescence signal upon interaction withthe double-stranded nucleic acid after excitation with light of asuitable wavelength. The dyes SybrGreen and SybrGold (Molecular Probes)have proven to be particularly suitable for this application.Intercalating dyes can alternatively be used.

C) Efficiency Correction by the Direct Determination of theAmplification Efficiencies

Absolute Quantification

In a preferred embodiment for the absolute quantification of a targetnucleic acid in a sample the method according to the invention comprisesthe following steps:

a) Determination of the amplification efficiencies of the target nucleicacid and of an internal or external standard as a function of therespective initial amounts under defined amplification conditions

b) Amplification of the target nucleic acid contained in the sample andof the internal or external standard under the same defined reactionconditions.

c) Measurement of the amplification of the target nucleic acid andstandard in real-time.

d) Determination of a defined signal threshold value.

e) Determination of the cycle numbers at which the signal thresholdvalue is in each case exceeded during the amplification of the targetnucleic acid and the standard.

f) Determination of the original copy number N(T)₀ of the target nucleicacid in the sample according to the formula${N(T)}_{0} = {{N(S)}_{0}*\frac{{E(S)}^{n\quad s}}{{E(T)}^{n\quad t}}}$

N(S)₀=the original amount of standard used

E(S)=the amplification efficiency of the standard for a particular cyclen at the respective time point of the detection averaged over theelapsed cycles

E(T)=the amplification efficiency of the target for a particular cycle nat the respective time point of the detection averaged over the elapsedcycles

ns=the cycle number at which the signal threshold value is exceeded bythe amplification of the standard nucleic acid and

nt=the cycle number at which the signal threshold value is exceeded bythe amplification of the target nucleic acid

Under these circumstances the calculation of N(T)₀ results in:N(T)_(n) =N(T)₀ *E ^(nt) andN(S)_(n) =N(S)₀ *E ^(ns)

Since an identical signal threshold value has been set for the targetand standard nucleic acid this approximates to:N(T)_(n) =N(S)_(n),

Hence the original copy number of target nucleic acid present in thesample is calculated according to the equation${N(T)}_{0} = {{N(S)}_{0}*\frac{{E(S)}^{n\quad s}}{{E(T)}^{n\quad t}}}$

In an alternative embodiment for the absolute quantification of a targetnucleic acid in a sample the method according to the invention comprisesthe following steps:

a) Determination of the amplification efficiencies of the target nucleicacid and of an internal or external standard as a function of therespective initial amounts under defined amplification conditions

b) Amplification of the target nucleic acid contained in the sample andof the internal or external standard under the same defined reactionconditions.

c) Measurement of the amplification of the target nucleic acid andstandard in real-time.

d) Determination of a defined signal threshold value.

e) Determination of the cycle numbers at which the signal thresholdvalue is in each case exceeded during the amplification of the targetnucleic acid and the standard.

f) Determination of the original copy number N(T)₀ of the target nucleicacid in the sample according to the formula${N(T)}_{0} = {{N(S)}_{0}*\frac{\prod\limits_{1 - n}^{\quad}\quad{E( S_{x} )}}{\prod\limits_{1 - n}^{\quad}\quad{E( T_{x} )}}}$

N(S)₀=the original amount of standard used

E(S_(n))=the amplification efficiency of the standard for an individualcycle x

E(T_(n))=the amplification efficiency of the target for an individualcycle x $\begin{matrix}{{\prod\limits_{1 - n}^{\quad}\quad{E( S_{x} )}} = {{the}\quad{product}\quad{of}\quad{the}\quad{efficiencies}\quad{determined}\quad{for}}} \\{{all}\quad{cycles}\quad{of}\quad{the}\quad{amplification}\quad{of}\quad{the}\quad{standard}\quad{until}} \\{{the}\quad{signal}\quad{threshold}\quad{value}\quad{is}} \\{{reached}\quad{at}\quad{cycle}\quad n}\end{matrix}$ $\begin{matrix}{{\prod\limits_{1 - n}^{\quad}\quad{E( T_{x} )}} = {{the}\quad{product}\quad{of}\quad{the}\quad{efficiencies}\quad{determined}\quad{for}}} \\{{all}\quad{cycles}\quad{of}\quad{the}\quad{amplification}\quad{of}\quad{the}\quad{target}} \\{{nucleic}\quad{acid}\quad{until}\quad{the}\quad{signal}\quad{threshold}} \\{{value}\quad{is}{\quad\quad}{reached}\quad{at}\quad{cycle}\quad n}\end{matrix}$

In this case the amplification efficiencies of the target nucleic acidand of the internal standard are preferably determined as describedabove by determining a cycle number at which a certain signal thresholdvalue is exceeded.

N(T)₀ is calculated according to the invention as follows:${N(T)}_{n} = {{{N(T)}_{0}*{E( T_{1} )}*\ldots*{E( T_{n} )}} = {{N( T_{0} )}*{\prod\limits_{1 - n}^{\quad}\quad{E( T_{x} )}}}}$and${N(S)}_{n} = {{{N(S)}_{0}*{E( S_{1} )}*\ldots*{E( S_{n} )}} = {{N( S_{0} )}*{\prod\limits_{1 - n}^{\quad}\quad{E( S_{x} )}}}}$

Since an identical signal threshold value has been set for the targetand standard nucleic acid this approximates to:N(T)_(n) =N(S)_(n),

Hence the original copy number of target nucleic acid present in thesample is calculated according to the equation${N(T)}_{0} = {{N(S)}_{0}*\frac{\prod\limits_{1 - n}^{\quad}\quad{E( S_{x} )}}{\prod\limits_{1 - n}^{\quad}\quad{E( T_{x} )}}}$

A disadvantage of this method is that the efficiencies of the firstcycles of each amplification reaction cannot be determined since theamount of amplified nucleic acid is still below the detection limit ofany detection system available in the prior art.

However, the efficiency of an earlier cycle can be approximated as thegeometric mean π of all the efficiencies determined for the followingcycles. Alternatively the non-determinable efficiency of an early cyclecan be equated with the efficiency determined for the first cycle inwhich an amplification product was detectable.

Relative Quantification.

A special embodiment of the relative quantification according to theinvention is a method for the quantification of a target nucleic acid ina sample relative to a reference nucleic acid comprising the followingsteps:

a) Determination of the amplification efficiencies of the target nucleicacid and of the reference nucleic acid as a function of the respectiveinitial amounts under defined amplification conditions

b) Amplification of the target nucleic acid contained in the sample andof the reference nucleic acid contained in the sample under the samedefined amplification conditions.

c) Measurement of the amplification of the target nucleic acid and thereference nucleic acid in real-time.

d) Determination of a defined signal threshold value.

e) Determination of the cycle numbers at which the signal thresholdvalue is in each case exceeded during the amplification of the targetnucleic acid and the reference nucleic acid.

f) Calculation of the original ratio of target nucleic acid andreference nucleic acid in the sample according to the formula${{N(T)}_{0}/{N(R)}_{0}} = \frac{{E(R)}^{nr}}{{E(T)}^{n\quad t}}$

N(T)₀=the original amount of target nucleic acid

N(R)₀=the original amount of reference nucleic acid

E(R)=the amplification efficiency of the reference nucleic acid averagedover the elapsed cycles at the respective detection time at a certaincycle n

E(T)=the amplification efficiency of the target nucleic acid averagedover the elapsed cycles at the respective detection time at a certaincycle n

nr=the cycle number at which the signal threshold value is exceeded bythe amplification of the reference nucleic acid

nt=the cycle number at which the signal threshold value is exceeded bythe amplification of the target nucleic acid

Under these circumstances the calculation of N(T)₀ results in:N(T)_(n) =N(T)₀ *E(T)^(nt) andN(R)_(n) =N(R)₀ *E(R)^(nr)

Since an identical signal threshold value has been set for the targetand standard nucleic acid this approximates to:N(T)_(n) =N(R)_(n),

Hence the original copy number of target nucleic acid present in thesample is calculated according to the equation${{N(T)}_{0}/{N(R)}_{0}} = \frac{{E(R)}^{nr}}{{E(T)}^{n\quad t}}$

In an alternative embodiment for the relative quantification of a targetnucleic acid in a sample the method according to the invention comprisesthe following steps:

a) Determination of the amplification efficiencies of the target nucleicacid and of the reference nucleic acid as a function of the initialamounts under defined amplification conditions

b) Amplification of the target nucleic acid contained in the sample andof the reference nucleic acid contained in the sample under the samedefined amplification conditions.

c) Measurement of the amplification of the target nucleic acid and ofthe reference nucleic acid in real-time.

d) Determination of a defined signal threshold value.

e) Determination of the cycle numbers at which the signal thresholdvalue is in each case exceeded during the amplification of the targetnucleic acid and the reference nucleic acid.

f) Determination of the original ratio of the target nucleic acid andreference nucleic acid in the sample according to the formula${{N(T)}_{0}/{N(R)}_{0}} = \frac{\prod\limits_{1 - n}{E( R_{x} )}}{\prod\limits_{1 - n}{E( T_{x} )}}$

N(T)₀=the original amount of target nucleic acid present in the sample

N(R)₀=the original amount of reference nucleic acid present in thesample

E(R_(n))=the amplification efficiency of the reference nucleic acid inan individual cycle x

E(T_(n))=the amplification efficiency of the target nucleic acid in anindividual cycle x $\begin{matrix}{{\prod\limits_{1 - n}{E(T)}} = \text{the~~product~~of~~the~~efficiencies~~determined~~for~~all}} \\{\text{cycles~~of~~the~~amplification~~of~~the~~target~~nucleic}} \\{\text{acid~~until~~the~~signal~~threshold~~value~~is~~reached~~at}} \\{\text{cycle}\quad n}\end{matrix}$ $\begin{matrix}{{\prod\limits_{1 - n}{E(R)}} = \text{the~~product~~of~~the~~efficiencies~~determined~~for~~all}} \\{\text{cycles~~of~~the~~amplification~~of~~the~~reference~~nucleic}} \\{\text{acid~~until~~the~~signal~~threshold~~value~~is~~reached~~at}} \\{\text{cycle}\quad n}\end{matrix}$

The ratio in step (f) is determined according to the invention asfollows: $\begin{matrix}{{N(T)}_{n} = {{{N(T)}_{0}^{*}{E( T_{1} )}^{*}\quad\ldots\quad{E( T_{n} )}} = {{N(T)}_{0}{\prod\limits_{\underset{1 - n}{n = 1}}{E( T_{x} )}}}}} & (1) \\{{N(R)}_{n} = {{{N(R)}_{0}^{*}{E( R_{1} )}^{*}\quad\ldots\quad{E( R_{n} )}} = {{N(R)}_{0}^{*}{\prod\limits_{1 - n}{E( R_{x} )}}}}} & (2)\end{matrix}$wherein N(T)_(n)=the amount of target-DNA at the signal threshold valueand N(R)_(n)=the amount of reference-DNA at the signal threshold value

from (1) and (2) it follows that: $\begin{matrix}{\frac{{N(T)}_{n}}{{N(R)}_{n}} = \frac{{N(T)}_{0}^{*}{\prod\limits_{1 - n}{E( T_{x} )}}}{{N(R)}_{0}^{*}{\prod\limits_{1 - n}{E( R_{x} )}}}} & (3)\end{matrix}$

It follows that: $\begin{matrix}{\frac{{N(T)}_{0}}{{N(R)}_{0}} = \frac{{N(T)}_{n}^{*}{\prod\limits_{1 - n}{E( R_{x} )}}}{{N(R)}_{n}^{*}{\prod\limits_{1 - n}{E( T_{x} )}}}} & (4)\end{matrix}$

Since an identical signal threshold value is set for the target nucleicacid and reference nucleic acid it can be assumed that approximatelyN(T)_(n) =N(R)_(n)

Under this condition and starting from equation (4) for the originalratio of target nucleic acid and reference nucleic acid, this results inthe equation $\begin{matrix}{{{N(T)}_{0}/{N(R)}_{0}} = {\prod\limits_{1 - n}{{E( R_{x} )}/{\prod\limits_{1 - n}{E( T_{x} )}}}}} & (5)\end{matrix}$

Similarly to the absolute quantification, the efficiency of an earlycycle that cannot be determined can be assumed to be the geometricaverage π of all the efficiencies determined for the following cycles.Alternatively the efficiency of an early cycle can be equated with theefficiency that was determined for the first cycle in which anamplification product was detectable.

Relative Quantification and Standardization by Reference to a Calibrator

The approximation N(T)_(n)=N(R)_(n) however only applies when the targetnucleic acid and reference nucleic acid are detected with differentsensitivities.

Due to the detection of the amplification products in this embodiment itis then advantageous to additionally carry out steps b), c), e) and f)of the method described above with a calibrator sample in order toeliminate systematic errors and subsequently to determine the ratio ofthe quotient determined for the sample and for the calibrator sample asa measure for the original amount of target nucleic acid in the sample.

Therefore according to the invention a calibrator sample is measured ina parallel reaction mixture and the ratio of the quotientsN(T)_(d)/N(R)₀ is determined for the sample and for the calibratorsample as a measure for the original amount of target nucleic acid inthe sample.

This results in the following from equation (4) using the indices

-   -   _(A) for the sample to be analysed and    -   _(K) for the calibrator sample $\begin{matrix}        {{\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}} = \frac{\frac{{N(R)}_{nA}^{*}{\prod\limits_{1 - n}{E_{A}( R_{x} )}}}{{N(T)}_{nA}^{*}{\prod\limits_{1 - n}{E_{A}( T_{x} )}}}}{\frac{{N(R)}_{nK}^{*}{\prod\limits_{1 - n}{E_{K}( R_{x} )}}}{{N(T)}_{nK}^{*}{\prod\limits_{1 - n}{E_{k}( T_{x} )}}}}} & (6)        \end{matrix}$

Due to the fact that an identical signal threshold value has beendefined the sample to be analysed and for the calibrator sample and thatidentical agents are used to detect target and reference amplicons inthe sample and in the calibrator sample, the ratio of the quotientsdetermined for the sample and for the calibrator sample are as follows:${\frac{{N(R)}_{nA}}{{N(T)}_{nA}}/\frac{{N(R)}_{nK}}{{N(T)}_{nK}}} = 1$

Hence the ratio of the quotients of the sample to be analysed and thecalibrator sample is: $\begin{matrix}{{\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}} = \frac{\prod\limits_{1 - n}{{E_{A}( R_{x} )}^{*}{\prod\limits_{1 - n}{E_{K}( T_{x} )}}}}{\prod\limits_{1 - n}{{E_{A}( T_{x} )}^{*}{\prod\limits_{1 - n}{E_{K}( R_{x} )}}}}} & (7)\end{matrix}$

Consequently a relative value can be obtained for the original copynumber of target nucleic acid in the sample in which systematic errorsdue to different amplification efficiencies as well as due to differentdetection sensitivities have been eliminated. The only requirement forthe accuracy of the determined value is the justified assumption thatunder absolutely identical buffer conditions the amplification anddetection efficiencies are also identical in the various reactionvessels.

D) Implicit Efficiency Correction When Using a Calibrator Sample

Furthermore the concentration-dependent efficiency correction accordingto the invention is also suitable for quantification methods in whichthe amplification efficiency is not determined directly but rather isincorporated indirectly in the quantification result.

This may for example be the case in methods for relative quantificationin which the result is standardized on the basis of a calibrator samplein order to eliminate the influence of different detection sensitivitiesfor the target and reference nucleic acid.

Hence the present invention also encompasses methods for the relativequantification of a target nucleic acid relative to a reference nucleicacid and standardized on the basis of a calibrator sample comprising thefollowing steps:

a) Preparing a common or two separate dilution series of target nucleicacid and reference nucleic acid.

b) Amplifying the various dilutions of target nucleic acid and referencenucleic acid under defined reaction conditions, the amplification of thenucleic acid being measured in real-time.

c) Setting defined signal threshold values for the target nucleic acidand reference nucleic acid.

d) Determining the cycle numbers Cp at which the signal threshold valuesdefined for the target nucleic acid and reference nucleic acid areexceeded in each dilution.

e) Determining a continuously differentiable function of the Cp valuesdetermined in d) as a function of a logarithm of the amounts used oftarget nucleic acid and determining a continuously differentiablefunction of the Cp values determined as a function of a logarithm of theamounts used of reference nucleic acid.

f) Determination of the Cp values for the target nucleic acid and thereference nucleic acid in the sample to be analysed as well as in acalibrator sample.

g) Assigning the Cp values measured in step f) to certain functionvalues of the functions determined in step e).

h) Calculating the quotients of the function values from g) of thetarget nucleic acid and reference nucleic acid for the sample to beanalysed as well as for the calibrator sample.

i) Determining the ratio of the quotients from h) as a measure for theamount of target DNA that was originally present in the sample.

Alternatively such a method according to the invention can be used forthe relative quantification of the target nucleic acid relative to areference nucleic acid and standardized on the basis of a calibratorsample which comprises the following steps:

a) Preparing a common or two separate dilution series of target nucleicacid and reference nucleic acid.

b) Amplifying the various dilutions of target nucleic acid and referencenucleic acid under defined reaction conditions, the amplification of thenucleic acid being measured in real-time.

c) Setting defined signal threshold values for the target nucleic acidand reference nucleic acid.

d) Determining the cycle numbers Cp at which the signal threshold valuesdefined for the target nucleic acid and reference nucleic acid areexceeded in each dilution.

e) Determining a continuously differentiable function of a logarithm ofthe amounts used of reference nucleic acid as a function of the Cpvalues determined in d) and determining a continuously differentiablefunction of a logarithm of the amounts used of reference nucleic acid asa function of the determined Cp.

f) Determination of the Cp values for the target nucleic acid and thereference nucleic acid in the sample to be analysed as well as in acalibrator sample.

g) Assigning the Cp values measured in step f) to certain functionvalues of the functions determined in step e).

h) Calculating the quotients of the function values from g) of thetarget nucleic acid and reference nucleic acid for the sample to beanalysed as well as for the calibrator sample.

i) Determining the ratio of the quotients from h) as a measure for theamount of target DNA that was originally present in the sample.

According to the invention the continuously differentiable functionsfrom step e) which can be linear or non-linear are determined with theaid of a polynomial fit preferably of the 3^(rd), 4^(th), 5^(th), 6^(th)or 7^(th) degree.

The extent to which the said continuously differentiable functions arelinear or non-linear depends on the initial concentrations of the targetand reference nucleic acid in the dilution series. With a low initialconcentration it can be probably assumed that there will not be a linearrelationship between the logarithm of the respective concentration andthe Cp values measured for the respective concentration. Apart from thisthe shape of the said functions depends on the respective experimentalconditions and on the respective target sequence and hence thesefunctions have to be determined empirically and cannot be derived on thebasis of theoretical considerations.

The described methods for standardization with the aid of a calibratorsample can also be used in particular when the amplificationefficiencies change in relation to the initial amounts of target nucleicacid or reference nucleic acid that are to be analysed. As a result thedependence of the amplification efficiencies on the respective originalcopy numbers of target nucleic acid and reference nucleic acid areindirectly taken into consideration. The quantification methodsaccording to the invention therefore enable even small initialconcentrations of target nucleic acid to be determined with highaccuracy.

The validity of such a quantification results from the followingconsiderations:

Functions are generated in steps a) to e) of the described method on thebasis of the cycle numbers (Cp values) measured for the dilution serieswhich are referred to as calibration curves in the following. Thecalibration curves are calculated from the individual measured values bymeans of mathematical methods for example with the aid of a polynomialfit. If the efficiency remains constant for the different initialconcentrations of target nucleic acid, the calibration curve is a linearfunction.

An example of such calibration curves is shown schematically in FIG. 1.The cycle number at which the defined signal threshold value is exceededis plotted on the abscissa of the graph. The logarithm of a certainrelative concentration is plotted on the ordinate of the graph (the basenumber of the logarithm can be selected at random provided it does notchange within the experimental reaction). In this connection therelative concentration is understood as a dimension without a unit whichis dependent on the respective detection efficiency but proportional tothe amount of target and reference nucleic acid that was actually used.

(In the example of FIG. 1 the amplification efficiency of the referencenucleic acid remains constant for various dilutions. However, incomparison the amplification efficiency of the target nucleic acid isincreased at low concentrations).

The cycle numbers (Cp values) for the target nucleic acid (Cp-Tar) andreference nucleic acid (Cp-Ref) at which the defined signal thresholdvalues are exceeded are determined for the sample to be analysed in thefollowing steps f) and g) of the described method. Function values log(Rconc(Tar)) and log (Rconc (Ref)) are assigned to the cycle numbersCp-Tar and Cp-Ref determined for the sample on the basis of thepreviously determined calibration curves.

In the case of a relative quantification it is additionally advantageousto eliminate the influence of different detection efficiencies for thetarget nucleic acid and reference nucleic acid. This can be achievedwith the aid of a so-called calibrator sample. Hence the Cp values forthe target nucleic acid and reference nucleic acid are also determinedfor a calibrator sample in the same manner as for the sample to beanalysed and also assigned corresponding function values.

However, in the following it is assumed that the detection efficiencyremains constant during an experiment i.e. an experimentally determinedrelative concentration is proportional to the copy number of target andreference nucleic acid that are actually present in the respectivesample. Thus the following firstly applies for any sample including thecalibrator:AConc(Tar)=K _(Tar) ×Rconc (Tar)  (1)AConc(Ref)=K _(Ref) ×Rconc (Ref)  (2)in which

AConc(Tar)=the actual copy number of target nucleic acid present in asample

AConc(Ref)=the actual copy number of reference nucleic acid present in asample

K_(Tar)=const

K_(Ref)=const

Rconc (Tar)=relative concentration of the target nucleic acid (without aunit)

Rconc (Ref)=relative concentration of the reference nucleic acid(without a unit)

The constants K_(Tar) and K_(Ref) are quantities whose absolute valuesdepend on the respective detection efficiency. In other words theseconstants take into consideration factors such as a different quantumyield of the fluorescent labels or different hybridization kinetics ofthe hybridization probes and are therefore usually not identical.

The following quotient is formed according to step h) of the methoddescribed above $\frac{{Rconc}({Tar})}{{Rconc}({Ref})}$from (1) and (2) it follows: $\begin{matrix}{\frac{{Rconc}\quad({Tar})}{{Rconc}\quad({Ref})} = \frac{K_{({Ref})} \times {Aconc}\quad({Tar})}{K_{({TAR})} \times {Aconc}\quad({Ref})}} & (3)\end{matrix}$

This equation applies equally to the sample to be analysed as well as tothe calibration sample since the same detection agent is used for bothsamples. $\begin{matrix}{\frac{{Rconc}\quad({Tar})_{{ca}\quad l}}{{Rconc}\quad({Ref})_{{ca}\quad l}} = {\frac{K({Ref})}{K({Tar})} \times \frac{{Aconc}\quad({Tar})_{{ca}\quad l}}{{Aconc}\quad({Ref})_{{ca}\quad l}}}} & (4)\end{matrix}$

According to step i) of the method described above the ratio of the twodetermined quotients is subsequently determined: $\begin{matrix}{\frac{\frac{{Rconc}\quad({Tar})}{{Rconc}\quad({Ref})}}{\frac{{Rconc}\quad({Tar})_{{ca}\quad l}}{{Rconc}\quad({Ref})_{{ca}\quad l}}} = \frac{\frac{{K({Ref})} \times {Aconc}\quad({Tar})}{{K({Tar})} \times {Aconc}\quad({Ref})}}{\frac{{K({Ref})} \times {Aconc}\quad({Tar})_{{ca}\quad l}}{{K({Tar})} \times {Aconc}\quad({Ref})_{{ca}\quad l}}}} & (5)\end{matrix}$

Consequently the constants that are dependent on the respectivedetection efficiency can be eliminated: $\begin{matrix}{\frac{\frac{{Rconc}\quad({Tar})}{{Rconc}\quad({Ref})}}{\frac{{Rconc}\quad({Tar})_{{ca}\quad l}}{{Rconc}\quad({Ref})_{{ca}\quad l}}} = \frac{\frac{{Aconc}\quad({Tar})}{{Aconc}\quad({Ref})}}{\frac{{Aconc}\quad({Tar})_{{ca}\quad l}}{{Aconc}\quad({Ref})_{{ca}\quad l}}}} & (6)\end{matrix}$

It follows that the ratios of the determined relative concentrations oftarget nucleic acid to reference nucleic acid standardized on the basisof the ratio of the relative concentrations of target nucleic acid toreference nucleic acid in the calibrator are identical to the ratios ofthe absolute copy numbers of target nucleic acid and reference nucleicacid in the individual samples to be analysed.

Hence this method according to the invention is an exact method for therelative quantification of nucleic acids in which

-   -   on the one hand, different efficiencies of PCR reactions are        taken into account without having to directly determine the        efficiency and    -   on the other hand, the influence of the detection efficiency        which depends on various uncontrollable factors is eliminated        due to the use of a calibrator sample.

The invention is further elucidated by the following examples:

EXAMPLE 1 Amplification of Cyclophylin A (CycA) and PorphobilinogenDeaminase (PBGD) cDNAs

cDNAs were synthesized with the aid of a reverse transcriptase reactionfrom 3 commercially available (Clontech) total RNAs isolated from a HeLacell line, adrenal gland tissue and brain tissue under the followingconditions:

-   -   1 μg total RNA    -   1×AMV reaction buffer    -   5 mM MgCl₂    -   1 mM deoxynucleotide mix    -   0.0625 mM randomized hexamers    -   50 units RNase    -   10 units AMV reverse transcriptase    -   ad 20 μl H₂O

All mixtures were incubated for 10 minutes at 25° C., 60 minutes at 42°C. and 5 minutes at 95° C. for the cDNA synthesis. Then they were cooledto 4° C.

-   -   Afterwards the amplification reaction was carried out which was        measured in real-time in the FRET HybProbe format on a        LightCycler instrument (Roche Diagnostics GmbH). Each mixture        was amplified under the following conditions:    -   1×LC-fast start DNA-master hybridization probes (Roche        Diagnostics GmbH)    -   3 m M MgCl₂    -   0.5 mM of each primer    -   0.2 μM fluorescein probe    -   0.2 μM LC-RED640 probe    -   ad 20 μl H₂O

Primers having SEQ. ID. NO:1 and SEQ. ID. NO: 2 were used to amplify theCycA sequence (Cyclophilin A). The CycA product was detected using afluorescein-labelled probe having SEQ. ID. NO: 3 and aLC-RED640-labelled probe having SEQ. ID. NO: 4. Primers having SEQ. ID.NO:5 and SEQ. ID. NO: 6 were used to amplify the PBGD sequence(porphobilinogen). The PBGD product was detected using afluorescein-labelled probe having SEQ. ID. NO: 7 and aLC-RED640-labelled probe having SEQ. ID. NO: 8.

The preparation was amplified under the following PCR conditions in theLightCycler: denaturation: 95° C. 10 min amplification: 45 x 95° C. 10sec 20.0° C./sec 55° C. 10 sec 20.0° C./sec 72° C. 15 sec  3.0° C./seccooling: 40° C. 30 sec

After each incubation at 55° C. a fluorescence measurement was carriedout according to the manufacturer's instructions. The signal thresholdvalue (Cp value) was determined as the maximum of the 2^(nd) derivativeof the amplification reaction as a function of the cycle number.

EXAMPLE 2 Determination of the Efficiency of the Amplification of CycAand PBGD

The cDNA synthesized from HeLa total RNA was diluted in 1:5 steps (atotal of 5 dilution steps) in order to determine the amplificationefficiencies of CycA and PBGD. A 3-fold determination of the signalthreshold value (Cp value) was carried out on the LightCycler for eachdilution step. This was carried out for CycA as well as for PBGD.

Two different functions were generated in order to determine the fitcoefficients in which the cycle number Cp was determined for eachconcentration as a function of the decadic logarithm of the cDNAconcentration used.

a) Generation of a linear function:

Assuming identical efficiencies for the various initial concentrationsof a nucleic acid, the two respective amplification efficiencies for thetarget nucleic acid and reference nucleic acid were determined accordingto the equation $E = {G{\frac{- 1}{f( {\log({conc})} )}.}}$

In this case f (log(conc)) was determined as the slope of the regressionline of the functions shown in FIGS. 2 a and 2 b. Thus an efficiencyE=2.62 was determined for the target nucleic acid CycA and an efficiencyE=1.97 was determined for the reference nucleic acid PBGD.

b) Generation of a non-linear function with the aid of a polynomial fitof the 4^(th) degree according to the invention

The same measured values were used to generate target and referencenucleic acid functions of the logarithm of the determined relativeconcentrations versus the measured Cp values by calculating a polynomialfit of the 4^(th) degree. These functions are shown in FIGS. 3 a (targetnucleic acid) and 3 b (reference nucleic acid).

The determined fit parameters for the target nucleic acid (CycA) were:

-   -   A(Offset)=11.3974946    -   B(linear)=−0.1    -   C(quadrat.)=−0.0721349    -   D=0.0044516    -   E=−8.214E-05

The determined fit parameters for the reference nucleic acid were:

-   -   A(Offset)=9.98347024    -   B(linear)=−0.29359011    -   C=0    -   D=0    -   E=0

As can be seen from the figures and the determined fit parameters, thisresults in an almost linear function for the reference nucleic acid.Consequently amplification of the reference nucleic acid in the measuredconcentration range occurs with largely constant efficiency.

In contrast a non-linear function was determined with the Cp valuesobtained for the target nucleic acid CycA. Hence the efficiency of theamplification reaction in the measured concentration range for CycA issignificantly dependent on the original copy number present in thesample.

EXAMPLE 3 Calibrator-standardized Determination of the Original Ratio ofTarget and Reference Nucleic Acid With and Without an Implied Correctionof the Amplification Efficiency

Under the conditions described in Example 1 the ratio determined of theoriginal amount of CycA and PBGD should be independent of the respectiveamplified amount of the sample material used. Hence the determination ofthe ratio of various amounts of sample RNA were used to check the effectof an efficiency correction on the basis of the measured values thatwere obtained.

The original ratios of target (CycA) and reference (PBGD) nucleic acidin adrenal gland RNA and brain RNA were determined using three dilutionsteps in each case of the cDNAs (duplicate determinations were carriedout for each dilution step). The quotient of the ratio of the relativeconcentrations CycA and PBGD were determined from the measured databetween the analysed sample and the calibrator sample. Total RNA fromHeLa cells was used as the calibrator. This determination was carriedout, on the one hand, with an assumed amplification efficiency of 2.00for CycA and PBGD, on the other hand, with the aid of the linear andnon-linear functions determined in Example 2. TABLE 1 shows thecalibrator-standardized ratios of target/reference nucleic acid implicitefficiency without efficiency correction with a efficiency correctionwith a non-linear fit correction linear fit function function adrenalgland 40 ng 1.03 1.18 1.41 adrenal gland 8 ng 2.21 1.79 1.19 adrenalgland 1.6 ng 6.00 4.17 1.93 mean 3.08 2.38 1.51 standard deviation2.5967 1.5799 0.3800 coefficient of variation 84.3% 66.4% 25.2% maximumerror in %*  483%  253%   62% (maximum value/minimum value − 1) × 100brain 40 ng 1.61 2.14 2.92 brain 8 ng 2.48 2.11 1.60 brain 1.6 ng 6.684.66 2.54 maximum error in %  315%  121%   82% mean 3.59 2.97 2.35standard deviation 2.7111 1.4637 0.6795 coefficient of variation 75.5%49.3% 28.9% maximum error in %* 75.5% 49.3% 28.9% (maximum value/minimumvalue − 1) × 100

As shown in Table 1 the values determined for the two sample RNAs(adrenal gland and brain tissues) after an inventive non-linearefficiency correction have a ca. three-fold lower coefficient ofvariation compared to the same values without an efficiency correctionand a ca. two-fold lower coefficient of variation than the same valueswith a linear efficiency correction. Also the percentage maximum errorof the calibrator-standardized target/reference ratios as a function ofthe initial concentration is also significantly reduced by the inventivenon-linear efficiency correction for the two target RNAs compared to thelinear efficiency correction or compared to the method without anefficiency correction. These results show that the inventive method isparticularly advantageous in methods in which a standardization iscarried out with the aid of calibrators.

The present invention is not to be limited in scope by the exemplifiedembodiments which are intended as illustrations of single aspects of theinvention. Various modifications of the invention in addition to thosedescribed herein will become apparent to those skilled in the art fromthe foregoing description and accompanying drawings. Such modificationsare intended to fall within the scope of the appended claims. Allpublications cited herein are incorporated by reference in theirentirety.

1-6. (Canceled)
 7. A method for the absolute quantification of a targetnucleic acid in a sample comprising the steps of: (a) determining theamplification efficiencies of the target nucleic acid and of an internalor external standard under defined amplification conditions by: (i)preparing a dilution series of the target nucleic acid and a dilutionseries of the internal or external standard; (ii) amplifying the targetnucleic acid and the internal or external standard under definedreaction conditions and measuring the amplification in real-time; (iii)setting a defined signal threshold value; (iv) determining, for eachdilution of the target nucleic acid and for each dilution of theinternal or external standard, the cycle number at which the signalthreshold value is exceeded; (v) determining a non-linear continuouslydifferentiable function of a logarithm of the copy number of targetnucleic acid and the internal or external standard used for theamplification as a function of the cycle number at which the signalthreshold value is exceeded; and (vi) calculating the amplificationefficiency of the target nucleic acid and the internal or externalstandard from said non-linear continuously differentiable function; (b)amplifying the target nucleic acid contained in the sample and theinternal or external standard under said defined reaction conditions;(c) measuring the amplification of the target nucleic acid and that ofthe internal or external standard in real time; and (d) calculating theoriginal copy number in the sample by correcting the copy number derivedfrom step (c) with the amplification efficiencies determined in step(a).
 8. A method for quantification of a target nucleic acid in a samplerelative to a reference nucleic acid comprising the steps of: (a)determining the amplification efficiencies of the target nucleic acidand of the reference nucleic acid under defined amplification conditionsby: (i) preparing a dilution series of the target nucleic acid and adilution series of the reference nucleic acid; (ii) amplifying thetarget nucleic acid and the reference nucleic acid under definedreaction conditions and measuring the amplification in real-time; (iii)setting a defined signal threshold value; (iv) determining, for eachdilution of the target nucleic acid and for each dilution of referencenucleic acid, the cycle number at which the signal threshold value isexceeded; (v) determining a non-linear continuously differentiablefunction of a logarithm of the copy number of target nucleic acid andthe reference nucleic acid used for the amplification as a function ofthe cycle number at which the signal threshold value is exceeded; and(vi) calculating the amplification efficiency of the target nucleic acidand the reference nucleic acid from said non-linear continuouslydifferentiable function; (b) amplifying the target nucleic acidcontained in the sample as well as the reference nucleic acid containedin the sample under said defined amplification conditions; (c) measuringthe amplification of the target nucleic acid and that of the referencenucleic acid in real time; and (d) calculating the original ratio oftarget nucleic acid and reference nucleic acid in the sample bycorrecting the ratio derived from step (c) with the amplificationefficiencies determined in step (a).
 9. A method for quantification of atarget nucleic acid relative to a reference nucleic acid andstandardized with a calibrator sample comprising the steps of: (a)preparing a common or two separate dilution series of target nucleicacid and reference nucleic acid; (b) amplifying the various dilutions oftarget nucleic acid and reference nucleic acid under defined reactionconditions, and measuring the amplification of the nucleic acids inreal-time; (c) setting defined signal threshold values for the targetnucleic acid and reference nucleic acid; (d) determining the cyclenumbers Cp at which the signal threshold values defined for the targetnucleic acid and reference nucleic acid are exceeded in each dilution;(e) determining a continuously differentiable function of the Cp valuesdetermined in step d) as a function of the logarithm of the amounts usedof target nucleic acid and determining a continuously differentiablefunction of the Cp values determined in step d) as a function of thelogarithm of the amounts used of reference nucleic acid; (f) determiningthe Cp values of the target nucleic acid and reference nucleic acid in asample to be analysed as well as in a calibrator sample; (g) assigningthe Cp values measured in step f) to particular values of the functionsdetermined in step e); (h) calculating the quotients of the functionvalues from step g) of the target nucleic acid and reference nucleicacid for the sample to be analysed as well as for the calibrator sample;and (i) determining the ratio of the two quotients from step h) as ameasure of the original amount of target nucleic acid contained in thesample to be analysed.
 10. A method for quantification of a targetnucleic acid relative to a reference nucleic acid and standardized witha calibrator sample comprising the steps of: (a) preparing a common ortwo separate dilution series of target nucleic acid and referencenucleic acid; (b) amplifying the various dilutions of target nucleicacid and reference nucleic acid under defined reaction conditions, andmeasuring the amplification of the nucleic acids in real-time; (c)setting defined signal threshold values for the target nucleic acid andreference nucleic acid; (d) determining the cycle numbers Cp at whichthe signal threshold values defined for the target nucleic acid andreference nucleic acid are exceeded in each dilution; (e) determining acontinuously differentiable function of the logarithm of the amountsused of target nucleic acid as a function of the Cp values determined instep d) and determining a continuously differentiable function of thelogarithm of the amounts used of reference nucleic acid as a function ofthe Cp values determined in step d); (f) determining the Cp values ofthe target nucleic acid and reference nucleic acid in a sample to beanalysed as well as in a calibrator sample; (g) assigning the Cp valuesmeasured in step f) to particular values of the functions determined instep e); (h) calculating the quotients of the function values from stepg) of the target nucleic acid and reference nucleic acid for the sampleto be analysed as well as for the calibrator sample; and (i) determiningthe ratio of the two quotients from step h) as a measure of the originalamount of target nucleic acid contained in the sample to be analysed.11. The method of claim 10, wherein the continuously differentiablefunctions from step e) are determined with a polynomial fit.
 12. Themethod of claim 10, wherein the amplified nucleic acids are detectedwith at least one fluorescently-labeled hybridization probe.
 13. Themethod of claim 12, wherein the amplified nucleic acids are detectedwith FRET hybridization probes, molecular beacons, or TAQMAN® probes.14. The method of claim 10, wherein the amplified nucleic acids aredetected with a DNA-binding dye.